Esileht
Juhuslik
Logi sisse
Sätted
Annetused
Vikiõpikute tiitelandmed
Lahtiütlused
Otsi
Matemaatika:Määramata integraal
Keel
Jälgi
Muuda
∫
x
d
x
=
x
+
C
{\displaystyle \int x\,\mathrm {d} x=x+C}
∫
x
α
d
x
=
x
α
+
1
α
+
1
+
C
{\displaystyle \int x^{\alpha }\,\mathrm {d} x={\frac {x^{\alpha }+1}{\alpha +1}}+C}
(α ≠ -1)
∫
1
x
d
x
=
l
n
|
x
|
+
C
{\displaystyle \int {\frac {1}{x}}\,\mathrm {d} x=ln|x|+C}
∫
x
e
d
x
=
e
+
C
{\displaystyle \int x^{e}\,\mathrm {d} x=e+C}
∫
a
x
d
x
=
a
x
l
n
(
a
)
+
C
{\displaystyle \int a^{x}\,\mathrm {d} x={\frac {a^{x}}{ln(a)}}+C}
∫
s
i
n
(
x
)
d
x
=
−
c
o
s
(
x
)
+
C
{\displaystyle \int sin(x)\,\mathrm {d} x=-cos(x)+C}
∫
c
o
s
(
x
)
d
x
=
s
i
n
(
x
)
+
C
{\displaystyle \int cos(x)\,\mathrm {d} x=sin(x)+C}
∫
1
c
o
s
2
(
x
)
d
x
=
t
a
n
(
x
)
+
C
{\displaystyle \int {\frac {1}{cos^{2}(x)}}\,\mathrm {d} x=tan(x)+C}
∫
1
s
i
n
2
(
x
)
d
x
=
−
c
o
t
(
x
)
+
C
{\displaystyle \int {\frac {1}{sin^{2}(x)}}\,\mathrm {d} x=-cot(x)+C}
∫
1
1
−
x
2
d
x
=
a
r
c
s
i
n
(
x
)
+
C
=
−
a
r
c
c
o
s
(
x
)
+
C
{\displaystyle \int {\frac {1}{\sqrt {1-x^{2}}}}\,\mathrm {d} x=arcsin(x)+C=-arccos(x)+C}
∫
1
1
−
x
2
d
x
=
a
r
c
t
a
n
(
x
)
+
C
{\displaystyle \int {\frac {1}{1-x^{2}}}\,\mathrm {d} x=arctan(x)+C}
∫
1
x
2
d
x
=
−
1
x
+
C
{\displaystyle \int {\frac {1}{x^{2}}}\,\mathrm {d} x=-{\frac {1}{x}}+C}
∫
1
2
x
d
x
=
x
+
C
{\displaystyle \int {\frac {1}{2{\sqrt {x}}}}\,\mathrm {d} x={\sqrt {x}}+C}
∫
a
∗
f
(
x
)
d
x
=
a
∫
f
(
x
)
d
x
{\displaystyle \int a*f(x)\,\mathrm {d} x=a\int f(x)\,\mathrm {d} x}
∫
[
f
(
x
)
+
g
(
x
)
]
d
x
=
∫
f
(
x
)
d
x
+
∫
g
(
x
)
d
x
{\displaystyle \int [f(x)+g(x)]\,\mathrm {d} x=\int f(x)\,\mathrm {d} x+\int g(x)\,\mathrm {d} x}
∫
f
(
a
∗
x
+
b
)
d
x
=
1
a
∗
f
(
a
∗
x
+
b
)
+
C
{\displaystyle \int f(a*x+b)\,\mathrm {d} x={\frac {1}{a}}*f(a*x+b)+C}
∫
d
(
c
o
s
(
x
)
)
=
c
o
s
(
x
)
+
C
{\displaystyle \int \,\mathrm {d} (cos(x))=cos(x)+C}
∫
u
+
v
x
d
x
=
∫
u
x
d
x
+
∫
v
x
d
x
{\displaystyle \int {\frac {u+v}{x}}\,\mathrm {d} x=\int {\frac {u}{x}}\,\mathrm {d} x+\int {\frac {v}{x}}\,\mathrm {d} x}